Haplodiploidy is a unique form of sex determination found in certain insect species, particularly in the order Hymenoptera, which includes honey bees, ants, and wasps. This system is characterized by having haploid males and diploid females. Let's explore the different options and understand why haplodiploidy is found in honey bees, ants, and wasps.

a) Grasshoppers and Cockroaches:
- Grasshoppers and cockroaches do not exhibit haplodiploidy. They have a typical system of sex determination where sex is determined by the presence of sex chromosomes. In grasshoppers, for example, males have two X chromosomes (XX), while females have one X and one Y chromosome (XY).

b) Birds and Reptiles:
- Birds and reptiles also do not display haplodiploidy. They have a different system of sex determination. In birds, males have two different sex chromosomes (ZZ), while females have two of the same sex chromosomes (ZW). Similarly, reptiles have different sex chromosomes determining male and female individuals.

c) Butterflies and Moths:
- Butterflies and moths do not possess haplodiploidy. They have a similar system of sex determination as grasshoppers and cockroaches, where sex is determined by the presence of sex chromosomes.

d) Honey bees, Ants, and Wasps:
- Honey bees, ants, and wasps are examples of hymenopteran insects that exhibit haplodiploidy. In these species, females develop from fertilized eggs, which are diploid and receive genetic material from both parents. On the other hand, males develop from unfertilized eggs, which are haploid and contain genetic material from the mother only.
- The key factor enabling haplodiploidy in these species is the mechanism of fertilization. When a queen bee, ant, or wasp mates with a male, she stores the sperm in a specialized organ called the spermatheca. The queen can then control the fertilization of eggs by selectively releasing sperm from the spermatheca. If an egg is fertilized, it develops into a female, while an unfertilized egg becomes a male.
- This unique reproductive strategy has several advantages for these species. Firstly, it ensures that all female workers in a colony are highly related, as they share the same father but have different combinations of the mother's genes. This relatedness promotes cooperation and altruistic behavior among workers, as they share a high proportion of their genetic material. Secondly, haplodiploidy reduces the potential for inbreeding, as the males only contribute their genetic material without having a direct genetic relationship with their sisters.
- It is important to note that not all hymenopteran insects exhibit haplodiploidy. Some species within the same order, such as certain parasitic wasps, do not follow this system and have a typical system of sex determination based on sex chromosomes.

In conclusion, haplodiploidy is found in honey bees, ants, and wasps, but not in grasshoppers, cockroaches, birds, reptiles, butterflies, or moths. This unique reproductive system contributes to the cooperative behavior and genetic relatedness observed in social insect colonies.